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#vectors

23 public questions tagged with this topic.

PHYSICS

A force F = 7 i + 3 j N acts at r = -2 i + 1 j m . What is the magnitude of the torque about the origin?

Given: A force F = 7 i + 3 j N acts at r = -2 i + 1 j m . What is the magnitude of the torque about the origin? These values define the system as per NCERT data. Formula: tau = r × F = beginvmatrix i & j & k -2 & 1 & 0 7 & 3 & 0 endvmatrix = k ((-2) × 3 - 1 × 7) = k (-6 - 7) = -13 k Nm. This is standard NCERT relation. Substitution & Calculation: Magnitude = 13 Nm . Result: The computed value matches expected outcome and confirms correct choice as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Relevant Physics topic covering fundamental principles,

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PHYSICS

A 7 kg object moves with a velocity of 3 i - 4 j m/s . What is the magnitude of the velocity of its nter of mass?

Given: A 7 kg object moves with a velocity of 3 i - 4 j m/s . What is the magnitude of the velocity of its nter of mass? These values define the system as per NCERT data. Formula: Magnitude = sqrt(3)² + (-4)² = sqrt9 + 16 = sqrt25 = 5 m/s .. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: For a single object, the nter of mass velocity equals the object’s velocity. Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

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PHYSICS

A force F = -2 i + 3 j N acts at r = 1 i + 2 j m . What is the torque about the origin?

Given: A force F = -2 i + 3 j N acts at r = 1 i + 2 j m . What is the torque about the origin? Formula: tau = r × F = beginvmatrix i & j & k 1 & 2 & 0 -2 & 3 & 0 endvmatrix = k (1 × 3 - 2 × (-2)) = k (3 + 4) = 7 k Nm .. Substitution: Substituting given values into formula as per NCERT 2026-27 method. Calculation: Simplifying step by step with proper SI units like m/s², J kg⁻¹ K⁻¹, 10⁻⁵, A m⁻¹ etc. Final Result: The computed value matches expected outcome and confirms correct choice as per latest NCERT 2026-27.

Ref: NCERT Physics Textbook - Latest Edition for Academic Session 2026-27 (Rationalized Textbook for Class XI and XII, continuing as per NCERT advisory for 2026-27),Topic: Fundamental laws, definitions and applications as per latest NCERT. The section explains governing laws, formulas like μ₀ = 4π.

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PHYSICS

A force F = 3 i + 4 j N acts at a point with position vector r = 2 i - 1 j m . What is the magnitude of the torque about

Given: A force F = 3 i + 4 j N acts at a point with position vector r = 2 i - 1 j m . What is the magnitude of the torque about the origin? These values define the system as per NCERT data. Formula: Torque: tau = r × F = beginvmatrix i & j & k 2 & -1 & 0 3 & 4 & 0 endvmatrix = k (2 × 4 - (-1) × 3) = k (8 + 3) = 11 k Nm. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: Magnitude = 11 Nm . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Laws of Motion, Work Energy Power, Gravitation and System of Particles, Topic: Newton's laws, work-energy theorem and rotational dynamics.

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ZOOLOGY

What is the role of a vector in recombinant DNA technology?

Vectors, such as plasmids, are used to carry and replicate foreign DNA inside host lls for cloning. This follows from NCERT principle where the relation explains the outcome clearly for students in simple steps.

Ref: NCERT Biology Textbook for Class XI and XII (Zoology section), Chapter: Principles of Inheritance, Molecular Basis of Inheritance and Biotechnology, Topic: Genetics, DNA techniques and applications.

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Center of Mass and System of Particles

Vectors a\=4i^−2j^ and b\=3i^+5j^ are given. What is the direction of a×b?

a×b = |i^j^k^4−20350| = k^(4×5−(−2)×3) = k^(20+6) = 26k^. Direction is along the positive z-axis (k^). As per NCERT, applying relevant law/formula with correct units and sign convention leads to k^. This satisfies dimensional consistency and physical conditions given, so option D is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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